Is it possible to make and run a successful speed fusion tunnel between 2 different locations without internet?
The connectivity medium between 2 locations is MPLS (local ISP MPLS connectivity without internet/Real IPs).

Yes, you can accomplish this with the Peplinks deployed as drop-in mode as long as there is connectivity between the sites. If there is no internet, fake DNS entries can be used on the WAN connections and you can use ping for the WAN health check method.